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© 2019 Robert A. Rucker 1
Understanding the 1988
Carbon Dating of the Shroud
by
Robert A. Rucker
August 16, 2019
www.shroudresearch.net1
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Outline
• Basic principles & terminology
• Examples of measurements
• Carbon dating of the Shroud
• Objections to the carbon dating
• Evidence for neutron absorption
• Conclusion
2
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The Mysteries of the Shroud
• Image
– Why can we see the image?
– How was the image formed?
• Date
– What is the date of the Shroud?
– What about the C14 dating?
• Blood
– How did it get onto the Shroud?
– Why is it still reddish? 3
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www.shroudresearch.net
On the RESEARCH page:
Paper 11: “Carbon Dating Problem, Part 1:
Background”
Paper 12: “Carbon Dating Problem, Part 2:
Statistical Analysis”
Paper 13: “Carbon Dating Problem, Part 3:
Neutron Absorption Hypothesis”
Paper 21: “Understanding the Statistical
Analysis of the Carbon Dating …"4
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Two Types of Measurement Error
• Random measurement errors
– Are always present in measurements
– Can be randomly positive or negative
– Effect can be minimized by averaging many
measurements, since effects will cancel
• Systematic measurement errors
– Are sometimes present, usually hard to detect
– Can be only positive, or only negative
– Are not minimized by many measurements
5
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Homogeneous vs.
Heterogeneous Samples
• “Homogeneous” means “the same”
• “Heterogeneous” means “different”
• Problem: Taking a small sample of an item
– To produce an accurate measurement for the
larger item, the small sample to be measured
must be the same as the larger item, i.e. it
must be representative.
• A homogeneous sample is representative.
• A heterogeneous sample is not. 6
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Example 1. Distance Measured with a Ruler
• Measure the distance between two points
• 3 people, each with a ruler
• Results: 95’3”, 90’1”, and 86’2”
• Option 1
– Average the values → 90’6”
– Ignore the differences
• Option 2
– Reject the data
– Investigate what caused the differences7
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Example 1. Distance Measured with a Ruler
• Random error estimated at 2” to 3”
• Systematic error
– rulers were longer than 12-inches
– 5%, 11%, and 16% longer
• True distance = 100 feet
• Average measured value = 90 feet 6 in.
• Systematic error or bias = - 9 feet 6 in.
8
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Example 2. Measurements in a Tank
• Assume a 2.17-meter (7’1”) high tank
filled with Uranium (U) in a liquid
• Assignment:
– Turn on the mixer in the tank for 24 hours
– Measure the concentration of U in the tank
– Take 3 measurements at different locations
– Send to three different laboratories
– Determine the total U in the tank from the
three measurements9
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Probability Distribution
10
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Example 2. Measurements in a Tank
• Measurement Results:
One Sigma Depth
Sample U (µg/g) Uncertainty cm inches
1 1200.8 30.7 5.0 2.0
2 1273.9 23.7 6.4 2.5
3 1303.5 17.2 7.7 3.0
• Question: What do the results mean?
Should the three values for U be averaged?
11
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121212
Laboratories Don’t Agree
• Difference between Lab 3 & Lab 1
Laboratory 3: 1303.5 17.2 µg/g
Laboratory 1: - 1200.8 30.7 µg/g
Difference = 102.7 34
Square root of 17.22 + 30.72 = 35.2
• 102.7 / 35.2 = 2.9 sigma difference
• Conclusion: the samples tested by
laboratories 3 and 1 were different
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131313
Measurements for Uranium in a Tank
1160
1180
1200
1220
1240
1260
1280
1300
1320
1340
4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0
Ura
niu
m C
on
cen
trat
ion
, µg
/g
Distance from the Top of the Tank, cm
Experimental values
Weighted least squares line
Assumes no bias
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141414
Measurements for Uranium in a Tank
1160
1180
1200
1220
1240
1260
1280
1300
1320
1340
4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0
Ura
niu
m C
on
cen
trat
ion
, µg
/g
Distance from the Top of the Tank, cm
Experimental values
Weighted least squares line
Assumes no bias
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151515
Measurements for Uranium in a Tank
1160
1180
1200
1220
1240
1260
1280
1300
1320
1340
4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0
Ura
niu
m C
on
cen
trat
ion
, µg
/g
Distance from the Top of the Tank, cm
Experimental values
Weighted least squares line
Assumes no bias
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161616
Measurements for Uranium in a Tank
1160
1180
1200
1220
1240
1260
1280
1300
1320
1340
4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0
Ura
niu
m C
on
cen
trat
ion
, µg
/g
Distance from the Top of the Tank, cm
Experimental values
Weighted least squares line
Assumes no bias
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171717
Measurements for Uranium in a Tank
1160
1180
1200
1220
1240
1260
1280
1300
1320
1340
4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0
Ura
niu
m C
on
cen
trat
ion
, µg
/g
Distance from the Top of the Tank, cm
Experimental values
Weighted least squares line
Assumes no bias
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Example 2. Measurements in a Tank
• Measurement Results:
One Sigma Depth
Sample U (µg/g) Uncertainty cm inches
1 1200.8 30.7 5.0 2.0
2 1273.9 23.7 6.4 2.5
3 1303.5 17.2 7.7 3.0
• Question: What do the results mean?
Should the three values for U be averaged?
18
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1988 Carbon Dating of the Shroud
• Measurement Results:
One Sigma Location
Laboratory Date AD Uncertainty cm inches
1 1200.8 30.7 5.0 2.0
2 1273.9 23.7 6.4 2.5
3 1303.5 17.2 7.7 3.0
• Question: What do the results mean?
Should the three dates be averaged?
19
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202020
• 6C12 atom has 6 protons and 6 neutrons
• 6C14 atom has 6 protons and 8 neutrons
What is a Neutron?
+
-
-
-
-
-
-
+
++
+
+
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75
80
85
90
95
100
105
110
115
120
-200 0 200 400 600 800 1000 1200 1400 1600 1800 2000
% o
f In
itia
l (C
14/C
12)
Rati
o
Years Since Death of the Plant or Animal
Without New C14
SOT dated to 690 years old as of 1950:1950 - 690 = 1260 AD
212121
Normal Decay for C14
1950 – 690 = 1260 AD
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Cutting of the Samples, 1988
22
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232323
Location of Samples for C14 Dating
3 samples cut from here
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242424
Location of Samples
A1ZOA2
Main Shroud
BackingPortion removed for textile
analysis by Prof. Gilbert Raes,
Nov. 24, 1973
Edge trimmed away by
Giovanni Riggi April 21,
1988 and retained by him
Side
Strip
Given to laboratory at Tucson, Arizona, in 1988
Given to laboratory at Zurich, Switzerland, in 1988
Given to laboratory at Oxford, England, in 1988
1988 portion believed to
be unused in the care of
the Archbishop of Turin.
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1988 Carbon Dating of the Shroud
• Damon, et al, “Radiocarbon Dating of the
Shroud of Turin”, Nature, Feb. 16, 1989
• Average of 3 laboratories = 1260 ± 31
• Correction for changing C14 in the
atmosphere → 1260 to 1390 AD, 95%
• “These results provide conclusive
evidence that the linen of the Shroud of
Turin is mediaeval.”
25
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Values by Carbon Dating (AD)
Oxford Zurich Arizona
1155 65 1217 61 1249 47 1249 47
1205 55 1228 56 1197 51 1318 49
1220 45 1271 51 1274 40 1410 37
1311 45 1344 41 1376 45
1315 57 .
1200.830.7 1273.923.7 1303.5 17.2
26
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Dating the Shroud
• Early 80’s → Shroud probably authentic
– Tradition claims it to be authentic
– Historical research allows it
– Blood marks → real body in the Shroud
– STURP → no normal process made image
– Image probably produced by radiation
• 1988 Carbon dating
– Average of measurements = 1260 ± 31 AD
– Corrected range =1260 to 1390 AD, 95%27
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Objections to the Carbon Dating
• Image could not be made in 1260-1390
• 13 other date indicators
• The different laboratories don’t agree
• Date is a function of the sample location
• Detailed statistical analysis
– Something had altered the samples
– The measured dates should be rejected
28
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The Technology Did Not Exist
to Make the Image in 1260-1390
• No pigment, carrier, brush strokes, etc.
• The image is a negative
• Contains 3D or topographical information.
• Only top 2 layers of fibers discolored
• Fiber discolored only 0.2 microns thick
• Discolored due to single electron bonds
changed into double electron bonds
29
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14 Date Indicators
1. Carbon Dating: 1260 to 1390 AD
2. Micro-particles of gold coins: < 1204
3. Hungarian Pray Codex: < 1192-1195
4. Invention of the spinning wheel: < 1200
5. 8 x 2 cubit size of the Shroud: ancient
6. Coins with image of the face: ~ 675
7. Sudarium of Oviedo: ~ 570
8. Ancient paintings: ~ 55030
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Ancient Coins
• I carry this coin in my wallet.
• An authentic Byzantine coin minted under
Constantine VIII in 1025 to 1028 AD
• This coin disproves the C14 dating
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3232
• Located in Oviedo, Spain
• In Jerusalem area, 570 AD
• In Oviedo since 840 AD
• Cloth 33 by 21 inches
• No image but blood pattern
similar to the Shroud
• Jesus’ face cloth, Jn.20:7
• C14 dated to 700 AD
Sudarium of Oviedo
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Christ Pantocrator, ~ 550 AD
33
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Date Indicators
9. Crucifixion outlawed in 337: < 337 AD
10. Ancient traditions: < second century
11. Unique stitch on the Shroud: < 100 AD
12. Image of Jesus on the Shroud: 30 to 33
13. Possible coin over one eye: 29 to 32
14. Reflectance & tensile strength of
linen as it ages: 33 BC ± 250
15. Radiation damage to linen: < 70 AD34
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353535
Laboratories Don’t Agree
• Difference between Arizona & Oxford:
Arizona: 1303.5 AD 17.2
Oxford: - 1200.8 AD 30.7
Difference = 102.7 35
Square root of 17.22 + 30.72 = 35.2
• 102.7 / 35.2 = 2.9 sigma difference
• Conslusion: the samples tested by
Arizona and Oxford were different
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363636
Dates are a Function of Sample Location
1160
1180
1200
1220
1240
1260
1280
1300
1320
1340
4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0
C1
4D
ate
, AD
Distance from the bottom of the Shroud, cm
Measured C14 datesWeighted least squares lineAssumes no bias
The best fit line is:
Y = 35.87 x + 1030.67
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Chi-Squared Statistical Analysis
• Probability that measurement
variation is due to:
• Only random measurement errors
= 1.4% probability
• Random errors + systematic bias
about 98% probability
• Something had changed the samples
• Measured values should be rejected37
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383838
Neutron Absorption Hypothesis
If neutrons were included in the burst
of radiation that caused the image,
then some of them would have been
absorbed in N14 in the Shroud to
produce new C14 atoms.
N14 + neutron → C14 + proton
This would cause the Shroud to be
C14 dated younger than its true age.
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75
80
85
90
95
100
105
110
115
120
-200 0 200 400 600 800 1000 1200 1400 1600 1800 2000
% o
f In
itia
l (C
14/C
12)
Rati
o
Age of the Shroud, (years)
With Neutron Absorption
Without Neutron Absorption
92% C14 remaining = 690 years old
393939
Effect of Producing New C14
1950 – 690 = 1260 AD
1950 – 1920 = 30 AD
![Page 40: Progress of Research on the Shroud of Turinshroudresearch.net/PP2-for-Ancaster-081619.pdf · •Difference between Lab 3 & Lab 1 Laboratory 3: 1303.5 17.2 µg/g Laboratory 1: - 1200.8](https://reader036.vdocuments.net/reader036/viewer/2022071100/5fd912d6083d341a8a1fe12c/html5/thumbnails/40.jpg)
404040
MCNP
• MCNP = Monte Carlo Neutron Particle
• Developed over the past six decades by
the Los Alamos National Laboratory
• Verified to be accurate by comparison
of calculated results with nuclear
experiments
![Page 41: Progress of Research on the Shroud of Turinshroudresearch.net/PP2-for-Ancaster-081619.pdf · •Difference between Lab 3 & Lab 1 Laboratory 3: 1303.5 17.2 µg/g Laboratory 1: - 1200.8](https://reader036.vdocuments.net/reader036/viewer/2022071100/5fd912d6083d341a8a1fe12c/html5/thumbnails/41.jpg)
414141
3D View Inside the Tomb
Body covered
by the Shroud
Face cloth
of Jesus
![Page 42: Progress of Research on the Shroud of Turinshroudresearch.net/PP2-for-Ancaster-081619.pdf · •Difference between Lab 3 & Lab 1 Laboratory 3: 1303.5 17.2 µg/g Laboratory 1: - 1200.8](https://reader036.vdocuments.net/reader036/viewer/2022071100/5fd912d6083d341a8a1fe12c/html5/thumbnails/42.jpg)
424242
C14 Date in Shroud Below the Body
![Page 43: Progress of Research on the Shroud of Turinshroudresearch.net/PP2-for-Ancaster-081619.pdf · •Difference between Lab 3 & Lab 1 Laboratory 3: 1303.5 17.2 µg/g Laboratory 1: - 1200.8](https://reader036.vdocuments.net/reader036/viewer/2022071100/5fd912d6083d341a8a1fe12c/html5/thumbnails/43.jpg)
75
80
85
90
95
100
105
110
115
120
-200 0 200 400 600 800 1000 1200 1400 1600 1800 2000
% o
f In
itia
l (C
14/C
12)
Rati
o
Age of the Shroud, (years before 1950)
Without New C14Arizona, 16.66% increase in C14Zurich, 16.24% increase in C14Oxford, 15.20% increase in C14
434343
Different Increases in C14 for
Each Sample Cause Different Dates
1950 – 1920 = 30 AD
![Page 44: Progress of Research on the Shroud of Turinshroudresearch.net/PP2-for-Ancaster-081619.pdf · •Difference between Lab 3 & Lab 1 Laboratory 3: 1303.5 17.2 µg/g Laboratory 1: - 1200.8](https://reader036.vdocuments.net/reader036/viewer/2022071100/5fd912d6083d341a8a1fe12c/html5/thumbnails/44.jpg)
444444
Large Tally Regions in the Tomb
Left side bench Right side bench
Shroud below the body
Shroud above the body
Shroud to the right of the body
Shroud to the left of the body
![Page 45: Progress of Research on the Shroud of Turinshroudresearch.net/PP2-for-Ancaster-081619.pdf · •Difference between Lab 3 & Lab 1 Laboratory 3: 1303.5 17.2 µg/g Laboratory 1: - 1200.8](https://reader036.vdocuments.net/reader036/viewer/2022071100/5fd912d6083d341a8a1fe12c/html5/thumbnails/45.jpg)
454545
Predicted C14 Dates (AD)
![Page 46: Progress of Research on the Shroud of Turinshroudresearch.net/PP2-for-Ancaster-081619.pdf · •Difference between Lab 3 & Lab 1 Laboratory 3: 1303.5 17.2 µg/g Laboratory 1: - 1200.8](https://reader036.vdocuments.net/reader036/viewer/2022071100/5fd912d6083d341a8a1fe12c/html5/thumbnails/46.jpg)
Neutron Absorption Hypothesis
• Is the only hypothesis consistent with
the 4 things we know about C14
dating as it applies to the Shroud
1. C14 date to 1260 ± 31, uncorrected
2. Slope of C14 date = ~ 36 years per cm
3. Range of dates = 1155 to 1410 AD
4. Date for Sudarium of Oviedo = 700 AD
46
![Page 47: Progress of Research on the Shroud of Turinshroudresearch.net/PP2-for-Ancaster-081619.pdf · •Difference between Lab 3 & Lab 1 Laboratory 3: 1303.5 17.2 µg/g Laboratory 1: - 1200.8](https://reader036.vdocuments.net/reader036/viewer/2022071100/5fd912d6083d341a8a1fe12c/html5/thumbnails/47.jpg)
Predicted Date (Change in C14)
47
2300 AD (4.3%)
4800 AD (41.2%)
4300 AD (32.9%)
1900 AD (-0.6%)
1260 AD (-8.0%)
1800 AD (-1.8%)
3700 AD (23.6%)
8500 AD (121%)
3100 AD (14.9%)
1500 AD (-5.3)
![Page 48: Progress of Research on the Shroud of Turinshroudresearch.net/PP2-for-Ancaster-081619.pdf · •Difference between Lab 3 & Lab 1 Laboratory 3: 1303.5 17.2 µg/g Laboratory 1: - 1200.8](https://reader036.vdocuments.net/reader036/viewer/2022071100/5fd912d6083d341a8a1fe12c/html5/thumbnails/48.jpg)
Testing the
Neutron Absorption Hypothesis
• C14 date at the elbows
1. ~ 4500 AD toward the back wall
2. ~ 3500 AD away from the back wall
• Detection of long half-life isotopes– C-14, Cl-36, Ca-41, Sc-45, Ni-59,
Zr-93, Nb-94, U-233, Pu-239
48